(II) A sample of (233)/(92) U(T (1)/(2)=1.59 ×10^5 yr) contains . 7.50 ×10^19 nuclei. (a) What

step 1 My dear student, so the formula which we will use to solve this problem is number of decay per s

(II) A sample of (233)/(92) U(T (1)/(2)=1.59 ×10^5 yr)...

(II) A sample of $\frac{233}{92} \mathrm{U}\left(T \frac{1}{2}=1.59 \times 10^{5} \text { yr) contains }\right.$ $7.50 \times 10^{19}$ nuclei. (a) What is the decay constant? (b) Approximately how many disintegrations will occur per minute?

Key Concepts

Radioactive Decay

Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. The process results in the transformation of the original nucleus into a different nucleus or a different energy state. This concept forms the basis for understanding how unstable nuclei diminish in number over time and is critical in fields such as nuclear physics, radiometric dating, and nuclear medicine.

Half-Life

Half-life is the time required for half of a sample of radioactive nuclei to decay. It is a characteristic property of a radioactive isotope and is independent of the initial amount present. Understanding half-life is crucial when calculating the decay constant and assessing the rate at which a radioactive substance decreases over time.

Decay Constant

The decay constant is a probability per unit time that a given nucleus will decay. It is mathematically related to the half-life by the equation ? = ln(2) / T?/?. This constant provides a measure of the rate of radioactive decay, enabling calculations of how many nuclei disintegrate over any time interval.

Activity

Activity is the measure of the number of disintegrations or decays per unit time in a radioactive sample. It is calculated using the formula A = ?N, where N is the number of radioactive nuclei present. Activity is often expressed in terms of decays per minute or per second and is a key parameter in both practical and theoretical applications of nuclear decay.

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